BALKAN-SL 2015 A5

Let $m, n$ be positive integers and $a, b$ positive real numbers different from $1$ such thath $m > n$ and $$\frac{a^{m+1}-1}{a^m-1} = \frac{b^{n+1}-1}{b^n-1} = c$$ . Prove that $a^m c^n > b^n c^{m}$ (Turkey)